Cycles having trouble calculating light from multiple emission objects
Try disabling multiple importance sampling in the material settings of the large emission plane.

I'm not sure exactly how multiple importance sampling decides what to do, but I suspect its deeming the giant emission plane much more likely to contribute to those samples than the tiny mesh light inside the lamp mesh.
As a result, it concentrates its efforts on the big mesh lamp, at the expense of the little mesh lamp. Disabling MIS on the big lamp takes it out of the importance sampling equation entirely, so special treatment is concentrated on the small lamp again.

You can also use a spot lamp in place of the tiny mesh lamp. In general, the lamp primitives are faster and less noisy than mesh lights.